Properties

Label 855.2.k.j.676.2
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.2
Root \(-0.398236 + 0.689765i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.j.406.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.898236 + 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.41478 q^{7} -1.38811 q^{8} +O(q^{10})\) \(q+(-0.898236 + 1.55579i) q^{2} +(-0.613656 - 1.06288i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.41478 q^{7} -1.38811 q^{8} +(-0.898236 - 1.55579i) q^{10} +4.35669 q^{11} +(-2.49135 - 4.31514i) q^{13} +(3.06728 - 5.31268i) q^{14} +(2.47416 - 4.28538i) q^{16} +(-0.0290433 + 0.0503046i) q^{17} +(-1.10304 - 4.21703i) q^{19} +1.22731 q^{20} +(-3.91334 + 6.77810i) q^{22} +(0.216041 + 0.374194i) q^{23} +(-0.500000 - 0.866025i) q^{25} +8.95127 q^{26} +(2.09550 + 3.62951i) q^{28} +(2.74750 + 4.75882i) q^{29} -0.592945 q^{31} +(3.05666 + 5.29428i) q^{32} +(-0.0521756 - 0.0903707i) q^{34} +(1.70739 - 2.95728i) q^{35} +6.62060 q^{37} +(7.55160 + 2.07179i) q^{38} +(0.694056 - 1.20214i) q^{40} +(0.0818718 - 0.141806i) q^{41} +(3.00242 - 5.20034i) q^{43} +(-2.67351 - 4.63066i) q^{44} -0.776222 q^{46} +(-5.54529 - 9.60473i) q^{47} +4.66070 q^{49} +1.79647 q^{50} +(-3.05766 + 5.29603i) q^{52} +(-2.69971 - 4.67603i) q^{53} +(-2.17835 + 3.77300i) q^{55} +4.74009 q^{56} -9.87163 q^{58} +(-1.72248 + 2.98342i) q^{59} +(-2.15698 - 3.73600i) q^{61} +(0.532604 - 0.922498i) q^{62} -1.08574 q^{64} +4.98270 q^{65} +(3.39217 + 5.87541i) q^{67} +0.0712905 q^{68} +(3.06728 + 5.31268i) q^{70} +(4.20501 - 7.28329i) q^{71} +(5.84804 - 10.1291i) q^{73} +(-5.94686 + 10.3003i) q^{74} +(-3.80532 + 3.76021i) q^{76} -14.8771 q^{77} +(-3.64303 + 6.30991i) q^{79} +(2.47416 + 4.28538i) q^{80} +(0.147080 + 0.254751i) q^{82} +16.1185 q^{83} +(-0.0290433 - 0.0503046i) q^{85} +(5.39377 + 9.34228i) q^{86} -6.04757 q^{88} +(-5.59024 - 9.68258i) q^{89} +(8.50740 + 14.7352i) q^{91} +(0.265150 - 0.459252i) q^{92} +19.9239 q^{94} +(4.20357 + 1.15325i) q^{95} +(-4.47355 + 7.74842i) q^{97} +(-4.18641 + 7.25107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.898236 + 1.55579i −0.635149 + 1.10011i 0.351335 + 0.936250i \(0.385728\pi\)
−0.986484 + 0.163860i \(0.947605\pi\)
\(3\) 0 0
\(4\) −0.613656 1.06288i −0.306828 0.531442i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −3.41478 −1.29066 −0.645332 0.763902i \(-0.723281\pi\)
−0.645332 + 0.763902i \(0.723281\pi\)
\(8\) −1.38811 −0.490771
\(9\) 0 0
\(10\) −0.898236 1.55579i −0.284047 0.491984i
\(11\) 4.35669 1.31359 0.656796 0.754069i \(-0.271911\pi\)
0.656796 + 0.754069i \(0.271911\pi\)
\(12\) 0 0
\(13\) −2.49135 4.31514i −0.690976 1.19680i −0.971519 0.236963i \(-0.923848\pi\)
0.280543 0.959841i \(-0.409485\pi\)
\(14\) 3.06728 5.31268i 0.819764 1.41987i
\(15\) 0 0
\(16\) 2.47416 4.28538i 0.618541 1.07134i
\(17\) −0.0290433 + 0.0503046i −0.00704405 + 0.0122006i −0.869526 0.493887i \(-0.835576\pi\)
0.862482 + 0.506088i \(0.168909\pi\)
\(18\) 0 0
\(19\) −1.10304 4.21703i −0.253054 0.967452i
\(20\) 1.22731 0.274435
\(21\) 0 0
\(22\) −3.91334 + 6.77810i −0.834326 + 1.44510i
\(23\) 0.216041 + 0.374194i 0.0450476 + 0.0780247i 0.887670 0.460480i \(-0.152323\pi\)
−0.842622 + 0.538505i \(0.818989\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 8.95127 1.75549
\(27\) 0 0
\(28\) 2.09550 + 3.62951i 0.396012 + 0.685913i
\(29\) 2.74750 + 4.75882i 0.510199 + 0.883690i 0.999930 + 0.0118169i \(0.00376151\pi\)
−0.489731 + 0.871873i \(0.662905\pi\)
\(30\) 0 0
\(31\) −0.592945 −0.106496 −0.0532480 0.998581i \(-0.516957\pi\)
−0.0532480 + 0.998581i \(0.516957\pi\)
\(32\) 3.05666 + 5.29428i 0.540346 + 0.935906i
\(33\) 0 0
\(34\) −0.0521756 0.0903707i −0.00894804 0.0154985i
\(35\) 1.70739 2.95728i 0.288601 0.499872i
\(36\) 0 0
\(37\) 6.62060 1.08842 0.544210 0.838949i \(-0.316830\pi\)
0.544210 + 0.838949i \(0.316830\pi\)
\(38\) 7.55160 + 2.07179i 1.22503 + 0.336089i
\(39\) 0 0
\(40\) 0.694056 1.20214i 0.109740 0.190075i
\(41\) 0.0818718 0.141806i 0.0127862 0.0221464i −0.859561 0.511032i \(-0.829263\pi\)
0.872348 + 0.488886i \(0.162597\pi\)
\(42\) 0 0
\(43\) 3.00242 5.20034i 0.457865 0.793045i −0.540983 0.841033i \(-0.681948\pi\)
0.998848 + 0.0479883i \(0.0152810\pi\)
\(44\) −2.67351 4.63066i −0.403047 0.698098i
\(45\) 0 0
\(46\) −0.776222 −0.114448
\(47\) −5.54529 9.60473i −0.808864 1.40099i −0.913651 0.406499i \(-0.866750\pi\)
0.104788 0.994495i \(-0.466584\pi\)
\(48\) 0 0
\(49\) 4.66070 0.665814
\(50\) 1.79647 0.254060
\(51\) 0 0
\(52\) −3.05766 + 5.29603i −0.424022 + 0.734427i
\(53\) −2.69971 4.67603i −0.370834 0.642303i 0.618860 0.785501i \(-0.287595\pi\)
−0.989694 + 0.143198i \(0.954261\pi\)
\(54\) 0 0
\(55\) −2.17835 + 3.77300i −0.293728 + 0.508752i
\(56\) 4.74009 0.633421
\(57\) 0 0
\(58\) −9.87163 −1.29621
\(59\) −1.72248 + 2.98342i −0.224248 + 0.388408i −0.956093 0.293062i \(-0.905326\pi\)
0.731846 + 0.681470i \(0.238659\pi\)
\(60\) 0 0
\(61\) −2.15698 3.73600i −0.276173 0.478346i 0.694257 0.719727i \(-0.255733\pi\)
−0.970430 + 0.241381i \(0.922400\pi\)
\(62\) 0.532604 0.922498i 0.0676408 0.117157i
\(63\) 0 0
\(64\) −1.08574 −0.135718
\(65\) 4.98270 0.618027
\(66\) 0 0
\(67\) 3.39217 + 5.87541i 0.414420 + 0.717796i 0.995367 0.0961450i \(-0.0306513\pi\)
−0.580948 + 0.813941i \(0.697318\pi\)
\(68\) 0.0712905 0.00864525
\(69\) 0 0
\(70\) 3.06728 + 5.31268i 0.366610 + 0.634986i
\(71\) 4.20501 7.28329i 0.499043 0.864368i −0.500956 0.865472i \(-0.667018\pi\)
0.999999 + 0.00110477i \(0.000351659\pi\)
\(72\) 0 0
\(73\) 5.84804 10.1291i 0.684461 1.18552i −0.289145 0.957285i \(-0.593371\pi\)
0.973606 0.228236i \(-0.0732958\pi\)
\(74\) −5.94686 + 10.3003i −0.691309 + 1.19738i
\(75\) 0 0
\(76\) −3.80532 + 3.76021i −0.436501 + 0.431325i
\(77\) −14.8771 −1.69541
\(78\) 0 0
\(79\) −3.64303 + 6.30991i −0.409873 + 0.709920i −0.994875 0.101111i \(-0.967760\pi\)
0.585003 + 0.811031i \(0.301094\pi\)
\(80\) 2.47416 + 4.28538i 0.276620 + 0.479120i
\(81\) 0 0
\(82\) 0.147080 + 0.254751i 0.0162423 + 0.0281325i
\(83\) 16.1185 1.76923 0.884617 0.466318i \(-0.154420\pi\)
0.884617 + 0.466318i \(0.154420\pi\)
\(84\) 0 0
\(85\) −0.0290433 0.0503046i −0.00315019 0.00545629i
\(86\) 5.39377 + 9.34228i 0.581625 + 1.00740i
\(87\) 0 0
\(88\) −6.04757 −0.644673
\(89\) −5.59024 9.68258i −0.592564 1.02635i −0.993886 0.110414i \(-0.964782\pi\)
0.401321 0.915937i \(-0.368551\pi\)
\(90\) 0 0
\(91\) 8.50740 + 14.7352i 0.891817 + 1.54467i
\(92\) 0.265150 0.459252i 0.0276438 0.0478804i
\(93\) 0 0
\(94\) 19.9239 2.05500
\(95\) 4.20357 + 1.15325i 0.431277 + 0.118321i
\(96\) 0 0
\(97\) −4.47355 + 7.74842i −0.454221 + 0.786733i −0.998643 0.0520780i \(-0.983416\pi\)
0.544422 + 0.838811i \(0.316749\pi\)
\(98\) −4.18641 + 7.25107i −0.422891 + 0.732469i
\(99\) 0 0
\(100\) −0.613656 + 1.06288i −0.0613656 + 0.106288i
\(101\) 1.09523 + 1.89700i 0.108980 + 0.188758i 0.915357 0.402643i \(-0.131908\pi\)
−0.806377 + 0.591401i \(0.798575\pi\)
\(102\) 0 0
\(103\) 10.4903 1.03364 0.516818 0.856095i \(-0.327117\pi\)
0.516818 + 0.856095i \(0.327117\pi\)
\(104\) 3.45827 + 5.98990i 0.339111 + 0.587358i
\(105\) 0 0
\(106\) 9.69991 0.942138
\(107\) −13.6911 −1.32357 −0.661783 0.749696i \(-0.730200\pi\)
−0.661783 + 0.749696i \(0.730200\pi\)
\(108\) 0 0
\(109\) 7.07679 12.2574i 0.677834 1.17404i −0.297798 0.954629i \(-0.596252\pi\)
0.975632 0.219413i \(-0.0704144\pi\)
\(110\) −3.91334 6.77810i −0.373122 0.646266i
\(111\) 0 0
\(112\) −8.44872 + 14.6336i −0.798329 + 1.38275i
\(113\) −13.2851 −1.24976 −0.624879 0.780722i \(-0.714852\pi\)
−0.624879 + 0.780722i \(0.714852\pi\)
\(114\) 0 0
\(115\) −0.432081 −0.0402918
\(116\) 3.37205 5.84056i 0.313087 0.542282i
\(117\) 0 0
\(118\) −3.09438 5.35963i −0.284861 0.493394i
\(119\) 0.0991765 0.171779i 0.00909150 0.0157469i
\(120\) 0 0
\(121\) 7.98075 0.725523
\(122\) 7.74991 0.701644
\(123\) 0 0
\(124\) 0.363864 + 0.630231i 0.0326760 + 0.0565964i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.84813 13.5934i −0.696409 1.20622i −0.969703 0.244285i \(-0.921447\pi\)
0.273295 0.961930i \(-0.411887\pi\)
\(128\) −5.13806 + 8.89938i −0.454145 + 0.786602i
\(129\) 0 0
\(130\) −4.47564 + 7.75203i −0.392539 + 0.679898i
\(131\) 5.86776 10.1633i 0.512669 0.887968i −0.487223 0.873277i \(-0.661990\pi\)
0.999892 0.0146910i \(-0.00467646\pi\)
\(132\) 0 0
\(133\) 3.76663 + 14.4002i 0.326608 + 1.24866i
\(134\) −12.1879 −1.05287
\(135\) 0 0
\(136\) 0.0403154 0.0698283i 0.00345702 0.00598773i
\(137\) 5.12860 + 8.88300i 0.438166 + 0.758926i 0.997548 0.0699840i \(-0.0222948\pi\)
−0.559382 + 0.828910i \(0.688962\pi\)
\(138\) 0 0
\(139\) −10.9044 18.8870i −0.924899 1.60197i −0.791723 0.610880i \(-0.790816\pi\)
−0.133176 0.991092i \(-0.542518\pi\)
\(140\) −4.19100 −0.354204
\(141\) 0 0
\(142\) 7.55418 + 13.0842i 0.633933 + 1.09800i
\(143\) −10.8540 18.7997i −0.907660 1.57211i
\(144\) 0 0
\(145\) −5.49501 −0.456336
\(146\) 10.5058 + 18.1966i 0.869469 + 1.50597i
\(147\) 0 0
\(148\) −4.06277 7.03693i −0.333958 0.578432i
\(149\) −10.3765 + 17.9727i −0.850079 + 1.47238i 0.0310582 + 0.999518i \(0.490112\pi\)
−0.881137 + 0.472862i \(0.843221\pi\)
\(150\) 0 0
\(151\) −14.9510 −1.21669 −0.608346 0.793672i \(-0.708167\pi\)
−0.608346 + 0.793672i \(0.708167\pi\)
\(152\) 1.53114 + 5.85370i 0.124192 + 0.474798i
\(153\) 0 0
\(154\) 13.3632 23.1457i 1.07683 1.86513i
\(155\) 0.296472 0.513505i 0.0238132 0.0412457i
\(156\) 0 0
\(157\) 0.0399391 0.0691765i 0.00318749 0.00552089i −0.864427 0.502758i \(-0.832319\pi\)
0.867615 + 0.497237i \(0.165652\pi\)
\(158\) −6.54460 11.3356i −0.520660 0.901810i
\(159\) 0 0
\(160\) −6.11331 −0.483300
\(161\) −0.737731 1.27779i −0.0581413 0.100704i
\(162\) 0 0
\(163\) 18.4845 1.44782 0.723909 0.689896i \(-0.242344\pi\)
0.723909 + 0.689896i \(0.242344\pi\)
\(164\) −0.200965 −0.0156927
\(165\) 0 0
\(166\) −14.4782 + 25.0770i −1.12373 + 1.94635i
\(167\) −9.34180 16.1805i −0.722890 1.25208i −0.959837 0.280560i \(-0.909480\pi\)
0.236946 0.971523i \(-0.423853\pi\)
\(168\) 0 0
\(169\) −5.91363 + 10.2427i −0.454894 + 0.787900i
\(170\) 0.104351 0.00800337
\(171\) 0 0
\(172\) −7.36982 −0.561943
\(173\) −4.29860 + 7.44540i −0.326817 + 0.566063i −0.981878 0.189512i \(-0.939309\pi\)
0.655062 + 0.755575i \(0.272643\pi\)
\(174\) 0 0
\(175\) 1.70739 + 2.95728i 0.129066 + 0.223550i
\(176\) 10.7792 18.6701i 0.812510 1.40731i
\(177\) 0 0
\(178\) 20.0854 1.50547
\(179\) 6.16587 0.460859 0.230429 0.973089i \(-0.425987\pi\)
0.230429 + 0.973089i \(0.425987\pi\)
\(180\) 0 0
\(181\) −10.0294 17.3715i −0.745481 1.29121i −0.949970 0.312343i \(-0.898886\pi\)
0.204488 0.978869i \(-0.434447\pi\)
\(182\) −30.5666 −2.26575
\(183\) 0 0
\(184\) −0.299889 0.519422i −0.0221081 0.0382923i
\(185\) −3.31030 + 5.73361i −0.243378 + 0.421543i
\(186\) 0 0
\(187\) −0.126533 + 0.219161i −0.00925300 + 0.0160267i
\(188\) −6.80581 + 11.7880i −0.496364 + 0.859728i
\(189\) 0 0
\(190\) −5.57002 + 5.50398i −0.404092 + 0.399301i
\(191\) −17.0701 −1.23515 −0.617573 0.786513i \(-0.711884\pi\)
−0.617573 + 0.786513i \(0.711884\pi\)
\(192\) 0 0
\(193\) −3.63576 + 6.29733i −0.261708 + 0.453292i −0.966696 0.255928i \(-0.917619\pi\)
0.704988 + 0.709219i \(0.250952\pi\)
\(194\) −8.03662 13.9198i −0.576995 0.999385i
\(195\) 0 0
\(196\) −2.86007 4.95378i −0.204291 0.353842i
\(197\) −3.59854 −0.256385 −0.128193 0.991749i \(-0.540918\pi\)
−0.128193 + 0.991749i \(0.540918\pi\)
\(198\) 0 0
\(199\) −10.7918 18.6919i −0.765008 1.32503i −0.940242 0.340506i \(-0.889402\pi\)
0.175234 0.984527i \(-0.443932\pi\)
\(200\) 0.694056 + 1.20214i 0.0490771 + 0.0850041i
\(201\) 0 0
\(202\) −3.93511 −0.276873
\(203\) −9.38211 16.2503i −0.658495 1.14055i
\(204\) 0 0
\(205\) 0.0818718 + 0.141806i 0.00571817 + 0.00990417i
\(206\) −9.42272 + 16.3206i −0.656512 + 1.13711i
\(207\) 0 0
\(208\) −24.6560 −1.70959
\(209\) −4.80559 18.3723i −0.332410 1.27084i
\(210\) 0 0
\(211\) −0.0351916 + 0.0609536i −0.00242269 + 0.00419622i −0.867234 0.497900i \(-0.834105\pi\)
0.864812 + 0.502097i \(0.167438\pi\)
\(212\) −3.31339 + 5.73896i −0.227564 + 0.394153i
\(213\) 0 0
\(214\) 12.2978 21.3004i 0.840661 1.45607i
\(215\) 3.00242 + 5.20034i 0.204763 + 0.354661i
\(216\) 0 0
\(217\) 2.02477 0.137451
\(218\) 12.7133 + 22.0200i 0.861051 + 1.49138i
\(219\) 0 0
\(220\) 5.34702 0.360496
\(221\) 0.289428 0.0194691
\(222\) 0 0
\(223\) 6.52703 11.3051i 0.437082 0.757049i −0.560381 0.828235i \(-0.689345\pi\)
0.997463 + 0.0711864i \(0.0226785\pi\)
\(224\) −10.4378 18.0788i −0.697405 1.20794i
\(225\) 0 0
\(226\) 11.9332 20.6689i 0.793783 1.37487i
\(227\) 7.75546 0.514748 0.257374 0.966312i \(-0.417143\pi\)
0.257374 + 0.966312i \(0.417143\pi\)
\(228\) 0 0
\(229\) 19.0597 1.25950 0.629751 0.776797i \(-0.283157\pi\)
0.629751 + 0.776797i \(0.283157\pi\)
\(230\) 0.388111 0.672228i 0.0255913 0.0443254i
\(231\) 0 0
\(232\) −3.81384 6.60577i −0.250391 0.433690i
\(233\) 6.26723 10.8552i 0.410580 0.711145i −0.584373 0.811485i \(-0.698660\pi\)
0.994953 + 0.100340i \(0.0319930\pi\)
\(234\) 0 0
\(235\) 11.0906 0.723470
\(236\) 4.22804 0.275222
\(237\) 0 0
\(238\) 0.178168 + 0.308596i 0.0115489 + 0.0200033i
\(239\) 15.7879 1.02123 0.510617 0.859808i \(-0.329417\pi\)
0.510617 + 0.859808i \(0.329417\pi\)
\(240\) 0 0
\(241\) −12.4166 21.5061i −0.799822 1.38533i −0.919732 0.392547i \(-0.871594\pi\)
0.119910 0.992785i \(-0.461739\pi\)
\(242\) −7.16860 + 12.4164i −0.460815 + 0.798155i
\(243\) 0 0
\(244\) −2.64729 + 4.58524i −0.169475 + 0.293540i
\(245\) −2.33035 + 4.03628i −0.148881 + 0.257869i
\(246\) 0 0
\(247\) −15.4490 + 15.2658i −0.982997 + 0.971342i
\(248\) 0.823073 0.0522652
\(249\) 0 0
\(250\) −0.898236 + 1.55579i −0.0568094 + 0.0983968i
\(251\) −1.65676 2.86958i −0.104573 0.181127i 0.808990 0.587822i \(-0.200014\pi\)
−0.913564 + 0.406695i \(0.866681\pi\)
\(252\) 0 0
\(253\) 0.941223 + 1.63025i 0.0591742 + 0.102493i
\(254\) 28.1979 1.76929
\(255\) 0 0
\(256\) −10.3161 17.8681i −0.644758 1.11675i
\(257\) 12.4325 + 21.5337i 0.775516 + 1.34323i 0.934504 + 0.355952i \(0.115843\pi\)
−0.158988 + 0.987280i \(0.550823\pi\)
\(258\) 0 0
\(259\) −22.6079 −1.40478
\(260\) −3.05766 5.29603i −0.189628 0.328446i
\(261\) 0 0
\(262\) 10.5413 + 18.2580i 0.651242 + 1.12798i
\(263\) 0.342686 0.593549i 0.0211309 0.0365998i −0.855267 0.518188i \(-0.826607\pi\)
0.876397 + 0.481588i \(0.159940\pi\)
\(264\) 0 0
\(265\) 5.39942 0.331684
\(266\) −25.7870 7.07470i −1.58110 0.433778i
\(267\) 0 0
\(268\) 4.16325 7.21097i 0.254311 0.440480i
\(269\) −5.58704 + 9.67704i −0.340648 + 0.590019i −0.984553 0.175086i \(-0.943980\pi\)
0.643905 + 0.765105i \(0.277313\pi\)
\(270\) 0 0
\(271\) 7.16308 12.4068i 0.435126 0.753661i −0.562180 0.827015i \(-0.690037\pi\)
0.997306 + 0.0733542i \(0.0233704\pi\)
\(272\) 0.143716 + 0.248923i 0.00871406 + 0.0150932i
\(273\) 0 0
\(274\) −18.4268 −1.11320
\(275\) −2.17835 3.77300i −0.131359 0.227521i
\(276\) 0 0
\(277\) −15.3518 −0.922397 −0.461199 0.887297i \(-0.652580\pi\)
−0.461199 + 0.887297i \(0.652580\pi\)
\(278\) 39.1789 2.34979
\(279\) 0 0
\(280\) −2.37004 + 4.10504i −0.141637 + 0.245323i
\(281\) −4.80640 8.32493i −0.286726 0.496624i 0.686300 0.727318i \(-0.259234\pi\)
−0.973026 + 0.230694i \(0.925900\pi\)
\(282\) 0 0
\(283\) −2.86255 + 4.95809i −0.170161 + 0.294728i −0.938476 0.345344i \(-0.887762\pi\)
0.768315 + 0.640072i \(0.221095\pi\)
\(284\) −10.3217 −0.612482
\(285\) 0 0
\(286\) 38.9979 2.30600
\(287\) −0.279574 + 0.484236i −0.0165027 + 0.0285836i
\(288\) 0 0
\(289\) 8.49831 + 14.7195i 0.499901 + 0.865854i
\(290\) 4.93582 8.54908i 0.289841 0.502019i
\(291\) 0 0
\(292\) −14.3547 −0.840048
\(293\) −23.3141 −1.36203 −0.681013 0.732271i \(-0.738460\pi\)
−0.681013 + 0.732271i \(0.738460\pi\)
\(294\) 0 0
\(295\) −1.72248 2.98342i −0.100287 0.173701i
\(296\) −9.19013 −0.534165
\(297\) 0 0
\(298\) −18.6412 32.2874i −1.07985 1.87036i
\(299\) 1.07647 1.86449i 0.0622536 0.107826i
\(300\) 0 0
\(301\) −10.2526 + 17.7580i −0.590950 + 1.02356i
\(302\) 13.4295 23.2606i 0.772781 1.33850i
\(303\) 0 0
\(304\) −20.8006 5.70668i −1.19300 0.327301i
\(305\) 4.31396 0.247017
\(306\) 0 0
\(307\) −4.24686 + 7.35577i −0.242381 + 0.419816i −0.961392 0.275183i \(-0.911262\pi\)
0.719011 + 0.694999i \(0.244595\pi\)
\(308\) 9.12944 + 15.8127i 0.520198 + 0.901010i
\(309\) 0 0
\(310\) 0.532604 + 0.922498i 0.0302499 + 0.0523943i
\(311\) −4.54326 −0.257625 −0.128812 0.991669i \(-0.541116\pi\)
−0.128812 + 0.991669i \(0.541116\pi\)
\(312\) 0 0
\(313\) 9.43148 + 16.3358i 0.533099 + 0.923354i 0.999253 + 0.0386503i \(0.0123058\pi\)
−0.466154 + 0.884703i \(0.654361\pi\)
\(314\) 0.0717495 + 0.124274i 0.00404906 + 0.00701317i
\(315\) 0 0
\(316\) 8.94227 0.503042
\(317\) 9.61822 + 16.6592i 0.540213 + 0.935677i 0.998891 + 0.0470741i \(0.0149897\pi\)
−0.458678 + 0.888602i \(0.651677\pi\)
\(318\) 0 0
\(319\) 11.9700 + 20.7327i 0.670193 + 1.16081i
\(320\) 0.542870 0.940279i 0.0303474 0.0525632i
\(321\) 0 0
\(322\) 2.65063 0.147714
\(323\) 0.244172 + 0.0669888i 0.0135861 + 0.00372735i
\(324\) 0 0
\(325\) −2.49135 + 4.31514i −0.138195 + 0.239361i
\(326\) −16.6034 + 28.7580i −0.919579 + 1.59276i
\(327\) 0 0
\(328\) −0.113647 + 0.196843i −0.00627511 + 0.0108688i
\(329\) 18.9359 + 32.7980i 1.04397 + 1.80821i
\(330\) 0 0
\(331\) 9.49306 0.521786 0.260893 0.965368i \(-0.415983\pi\)
0.260893 + 0.965368i \(0.415983\pi\)
\(332\) −9.89121 17.1321i −0.542851 0.940245i
\(333\) 0 0
\(334\) 33.5646 1.83657
\(335\) −6.78434 −0.370668
\(336\) 0 0
\(337\) −11.8854 + 20.5860i −0.647437 + 1.12139i 0.336296 + 0.941756i \(0.390826\pi\)
−0.983733 + 0.179637i \(0.942508\pi\)
\(338\) −10.6237 18.4007i −0.577851 1.00087i
\(339\) 0 0
\(340\) −0.0356453 + 0.0617394i −0.00193314 + 0.00334829i
\(341\) −2.58328 −0.139892
\(342\) 0 0
\(343\) 7.98819 0.431322
\(344\) −4.16769 + 7.21866i −0.224707 + 0.389204i
\(345\) 0 0
\(346\) −7.72232 13.3755i −0.415155 0.719069i
\(347\) 14.0069 24.2607i 0.751932 1.30238i −0.194953 0.980813i \(-0.562455\pi\)
0.946885 0.321572i \(-0.104211\pi\)
\(348\) 0 0
\(349\) 0.00959659 0.000513694 0.000256847 1.00000i \(-0.499918\pi\)
0.000256847 1.00000i \(0.499918\pi\)
\(350\) −6.13455 −0.327906
\(351\) 0 0
\(352\) 13.3169 + 23.0656i 0.709793 + 1.22940i
\(353\) −6.08582 −0.323915 −0.161958 0.986798i \(-0.551781\pi\)
−0.161958 + 0.986798i \(0.551781\pi\)
\(354\) 0 0
\(355\) 4.20501 + 7.28329i 0.223179 + 0.386557i
\(356\) −6.86097 + 11.8836i −0.363631 + 0.629827i
\(357\) 0 0
\(358\) −5.53841 + 9.59281i −0.292714 + 0.506996i
\(359\) −8.91042 + 15.4333i −0.470274 + 0.814538i −0.999422 0.0339910i \(-0.989178\pi\)
0.529148 + 0.848529i \(0.322512\pi\)
\(360\) 0 0
\(361\) −16.5666 + 9.30307i −0.871927 + 0.489635i
\(362\) 36.0352 1.89397
\(363\) 0 0
\(364\) 10.4412 18.0848i 0.547269 0.947898i
\(365\) 5.84804 + 10.1291i 0.306100 + 0.530181i
\(366\) 0 0
\(367\) 2.45095 + 4.24517i 0.127938 + 0.221596i 0.922878 0.385093i \(-0.125831\pi\)
−0.794939 + 0.606689i \(0.792497\pi\)
\(368\) 2.13808 0.111455
\(369\) 0 0
\(370\) −5.94686 10.3003i −0.309163 0.535485i
\(371\) 9.21891 + 15.9676i 0.478622 + 0.828997i
\(372\) 0 0
\(373\) −12.9995 −0.673090 −0.336545 0.941667i \(-0.609258\pi\)
−0.336545 + 0.941667i \(0.609258\pi\)
\(374\) −0.227313 0.393717i −0.0117541 0.0203586i
\(375\) 0 0
\(376\) 7.69748 + 13.3324i 0.396967 + 0.687567i
\(377\) 13.6900 23.7117i 0.705070 1.22122i
\(378\) 0 0
\(379\) 16.7313 0.859427 0.429713 0.902965i \(-0.358615\pi\)
0.429713 + 0.902965i \(0.358615\pi\)
\(380\) −1.35377 5.17561i −0.0694470 0.265503i
\(381\) 0 0
\(382\) 15.3330 26.5575i 0.784502 1.35880i
\(383\) −14.9461 + 25.8875i −0.763712 + 1.32279i 0.177213 + 0.984172i \(0.443292\pi\)
−0.940925 + 0.338615i \(0.890042\pi\)
\(384\) 0 0
\(385\) 7.43856 12.8840i 0.379104 0.656628i
\(386\) −6.53155 11.3130i −0.332447 0.575815i
\(387\) 0 0
\(388\) 10.9809 0.557471
\(389\) −15.8669 27.4822i −0.804483 1.39340i −0.916640 0.399714i \(-0.869109\pi\)
0.112157 0.993691i \(-0.464224\pi\)
\(390\) 0 0
\(391\) −0.0250982 −0.00126927
\(392\) −6.46957 −0.326763
\(393\) 0 0
\(394\) 3.23234 5.59857i 0.162843 0.282052i
\(395\) −3.64303 6.30991i −0.183301 0.317486i
\(396\) 0 0
\(397\) −16.9999 + 29.4447i −0.853202 + 1.47779i 0.0251017 + 0.999685i \(0.492009\pi\)
−0.878303 + 0.478104i \(0.841324\pi\)
\(398\) 38.7742 1.94358
\(399\) 0 0
\(400\) −4.94833 −0.247416
\(401\) 4.55045 7.88161i 0.227239 0.393589i −0.729750 0.683714i \(-0.760364\pi\)
0.956989 + 0.290125i \(0.0936970\pi\)
\(402\) 0 0
\(403\) 1.47723 + 2.55864i 0.0735861 + 0.127455i
\(404\) 1.34419 2.32821i 0.0668761 0.115833i
\(405\) 0 0
\(406\) 33.7094 1.67297
\(407\) 28.8439 1.42974
\(408\) 0 0
\(409\) 13.9425 + 24.1491i 0.689411 + 1.19409i 0.972029 + 0.234862i \(0.0754639\pi\)
−0.282618 + 0.959233i \(0.591203\pi\)
\(410\) −0.294161 −0.0145276
\(411\) 0 0
\(412\) −6.43741 11.1499i −0.317148 0.549317i
\(413\) 5.88188 10.1877i 0.289428 0.501305i
\(414\) 0 0
\(415\) −8.05924 + 13.9590i −0.395613 + 0.685221i
\(416\) 15.2304 26.3798i 0.746731 1.29338i
\(417\) 0 0
\(418\) 32.9000 + 9.02615i 1.60919 + 0.441483i
\(419\) 31.5961 1.54357 0.771785 0.635884i \(-0.219364\pi\)
0.771785 + 0.635884i \(0.219364\pi\)
\(420\) 0 0
\(421\) −6.42177 + 11.1228i −0.312978 + 0.542094i −0.979006 0.203833i \(-0.934660\pi\)
0.666028 + 0.745927i \(0.267993\pi\)
\(422\) −0.0632207 0.109502i −0.00307754 0.00533045i
\(423\) 0 0
\(424\) 3.74750 + 6.49086i 0.181995 + 0.315224i
\(425\) 0.0580867 0.00281762
\(426\) 0 0
\(427\) 7.36561 + 12.7576i 0.356447 + 0.617384i
\(428\) 8.40161 + 14.5520i 0.406107 + 0.703398i
\(429\) 0 0
\(430\) −10.7875 −0.520221
\(431\) −16.6064 28.7630i −0.799900 1.38547i −0.919681 0.392667i \(-0.871553\pi\)
0.119781 0.992800i \(-0.461781\pi\)
\(432\) 0 0
\(433\) −3.66146 6.34183i −0.175958 0.304769i 0.764534 0.644583i \(-0.222969\pi\)
−0.940493 + 0.339814i \(0.889636\pi\)
\(434\) −1.81872 + 3.15012i −0.0873016 + 0.151211i
\(435\) 0 0
\(436\) −17.3709 −0.831914
\(437\) 1.33968 1.32380i 0.0640857 0.0633259i
\(438\) 0 0
\(439\) −11.4327 + 19.8020i −0.545651 + 0.945096i 0.452914 + 0.891554i \(0.350384\pi\)
−0.998566 + 0.0535417i \(0.982949\pi\)
\(440\) 3.02379 5.23735i 0.144153 0.249681i
\(441\) 0 0
\(442\) −0.259975 + 0.450290i −0.0123657 + 0.0214181i
\(443\) −7.40824 12.8315i −0.351976 0.609641i 0.634619 0.772825i \(-0.281157\pi\)
−0.986596 + 0.163184i \(0.947824\pi\)
\(444\) 0 0
\(445\) 11.1805 0.530006
\(446\) 11.7256 + 20.3094i 0.555225 + 0.961677i
\(447\) 0 0
\(448\) 3.70756 0.175166
\(449\) 41.8708 1.97600 0.988002 0.154441i \(-0.0493576\pi\)
0.988002 + 0.154441i \(0.0493576\pi\)
\(450\) 0 0
\(451\) 0.356690 0.617805i 0.0167959 0.0290913i
\(452\) 8.15249 + 14.1205i 0.383461 + 0.664174i
\(453\) 0 0
\(454\) −6.96623 + 12.0659i −0.326942 + 0.566279i
\(455\) −17.0148 −0.797666
\(456\) 0 0
\(457\) 38.4845 1.80023 0.900114 0.435655i \(-0.143483\pi\)
0.900114 + 0.435655i \(0.143483\pi\)
\(458\) −17.1201 + 29.6530i −0.799972 + 1.38559i
\(459\) 0 0
\(460\) 0.265150 + 0.459252i 0.0123627 + 0.0214128i
\(461\) −13.9830 + 24.2192i −0.651251 + 1.12800i 0.331568 + 0.943431i \(0.392422\pi\)
−0.982820 + 0.184569i \(0.940911\pi\)
\(462\) 0 0
\(463\) 12.5403 0.582797 0.291399 0.956602i \(-0.405879\pi\)
0.291399 + 0.956602i \(0.405879\pi\)
\(464\) 27.1911 1.26232
\(465\) 0 0
\(466\) 11.2589 + 19.5010i 0.521559 + 0.903366i
\(467\) 24.4525 1.13153 0.565764 0.824567i \(-0.308581\pi\)
0.565764 + 0.824567i \(0.308581\pi\)
\(468\) 0 0
\(469\) −11.5835 20.0632i −0.534877 0.926434i
\(470\) −9.96196 + 17.2546i −0.459511 + 0.795896i
\(471\) 0 0
\(472\) 2.39099 4.14132i 0.110054 0.190620i
\(473\) 13.0806 22.6563i 0.601447 1.04174i
\(474\) 0 0
\(475\) −3.10053 + 3.06377i −0.142262 + 0.140575i
\(476\) −0.243441 −0.0111581
\(477\) 0 0
\(478\) −14.1813 + 24.5626i −0.648635 + 1.12347i
\(479\) 3.27876 + 5.67898i 0.149810 + 0.259479i 0.931157 0.364618i \(-0.118800\pi\)
−0.781347 + 0.624097i \(0.785467\pi\)
\(480\) 0 0
\(481\) −16.4942 28.5688i −0.752071 1.30263i
\(482\) 44.6121 2.03202
\(483\) 0 0
\(484\) −4.89744 8.48261i −0.222611 0.385573i
\(485\) −4.47355 7.74842i −0.203134 0.351838i
\(486\) 0 0
\(487\) −12.6305 −0.572341 −0.286170 0.958179i \(-0.592382\pi\)
−0.286170 + 0.958179i \(0.592382\pi\)
\(488\) 2.99413 + 5.18598i 0.135538 + 0.234758i
\(489\) 0 0
\(490\) −4.18641 7.25107i −0.189123 0.327570i
\(491\) 6.46604 11.1995i 0.291808 0.505427i −0.682429 0.730952i \(-0.739076\pi\)
0.974237 + 0.225525i \(0.0724098\pi\)
\(492\) 0 0
\(493\) −0.319187 −0.0143755
\(494\) −9.87359 37.7478i −0.444234 1.69835i
\(495\) 0 0
\(496\) −1.46704 + 2.54099i −0.0658722 + 0.114094i
\(497\) −14.3592 + 24.8708i −0.644097 + 1.11561i
\(498\) 0 0
\(499\) 14.9627 25.9162i 0.669824 1.16017i −0.308129 0.951345i \(-0.599703\pi\)
0.977953 0.208825i \(-0.0669639\pi\)
\(500\) −0.613656 1.06288i −0.0274435 0.0475336i
\(501\) 0 0
\(502\) 5.95263 0.265679
\(503\) −15.1592 26.2565i −0.675914 1.17072i −0.976201 0.216869i \(-0.930416\pi\)
0.300287 0.953849i \(-0.402918\pi\)
\(504\) 0 0
\(505\) −2.19046 −0.0974744
\(506\) −3.38176 −0.150338
\(507\) 0 0
\(508\) −9.63211 + 16.6833i −0.427356 + 0.740202i
\(509\) 13.2252 + 22.9067i 0.586197 + 1.01532i 0.994725 + 0.102577i \(0.0327088\pi\)
−0.408528 + 0.912746i \(0.633958\pi\)
\(510\) 0 0
\(511\) −19.9697 + 34.5886i −0.883409 + 1.53011i
\(512\) 16.5130 0.729779
\(513\) 0 0
\(514\) −44.6692 −1.97027
\(515\) −5.24513 + 9.08483i −0.231128 + 0.400325i
\(516\) 0 0
\(517\) −24.1591 41.8448i −1.06252 1.84033i
\(518\) 20.3072 35.1731i 0.892247 1.54542i
\(519\) 0 0
\(520\) −6.91654 −0.303310
\(521\) 3.32486 0.145665 0.0728324 0.997344i \(-0.476796\pi\)
0.0728324 + 0.997344i \(0.476796\pi\)
\(522\) 0 0
\(523\) −8.88844 15.3952i −0.388664 0.673186i 0.603606 0.797283i \(-0.293730\pi\)
−0.992270 + 0.124097i \(0.960397\pi\)
\(524\) −14.4032 −0.629205
\(525\) 0 0
\(526\) 0.615626 + 1.06630i 0.0268426 + 0.0464927i
\(527\) 0.0172211 0.0298278i 0.000750163 0.00129932i
\(528\) 0 0
\(529\) 11.4067 19.7569i 0.495941 0.858996i
\(530\) −4.84995 + 8.40037i −0.210669 + 0.364889i
\(531\) 0 0
\(532\) 12.9943 12.8403i 0.563376 0.556696i
\(533\) −0.815884 −0.0353399
\(534\) 0 0
\(535\) 6.84553 11.8568i 0.295958 0.512615i
\(536\) −4.70871 8.15573i −0.203385 0.352274i
\(537\) 0 0
\(538\) −10.0370 17.3845i −0.432724 0.749500i
\(539\) 20.3052 0.874608
\(540\) 0 0
\(541\) 17.7241 + 30.6991i 0.762021 + 1.31986i 0.941808 + 0.336153i \(0.109126\pi\)
−0.179787 + 0.983706i \(0.557541\pi\)
\(542\) 12.8683 + 22.2885i 0.552740 + 0.957374i
\(543\) 0 0
\(544\) −0.355102 −0.0152249
\(545\) 7.07679 + 12.2574i 0.303136 + 0.525048i
\(546\) 0 0
\(547\) −9.90142 17.1498i −0.423354 0.733271i 0.572911 0.819618i \(-0.305814\pi\)
−0.996265 + 0.0863465i \(0.972481\pi\)
\(548\) 6.29440 10.9022i 0.268883 0.465720i
\(549\) 0 0
\(550\) 7.82667 0.333730
\(551\) 17.0375 16.8355i 0.725820 0.717214i
\(552\) 0 0
\(553\) 12.4401 21.5469i 0.529008 0.916269i
\(554\) 13.7895 23.8841i 0.585860 1.01474i
\(555\) 0 0
\(556\) −13.3831 + 23.1802i −0.567570 + 0.983061i
\(557\) −13.6340 23.6148i −0.577692 1.00059i −0.995743 0.0921684i \(-0.970620\pi\)
0.418052 0.908423i \(-0.362713\pi\)
\(558\) 0 0
\(559\) −29.9203 −1.26549
\(560\) −8.44872 14.6336i −0.357024 0.618383i
\(561\) 0 0
\(562\) 17.2691 0.728455
\(563\) 28.6245 1.20638 0.603190 0.797598i \(-0.293896\pi\)
0.603190 + 0.797598i \(0.293896\pi\)
\(564\) 0 0
\(565\) 6.64256 11.5052i 0.279454 0.484029i
\(566\) −5.14250 8.90706i −0.216155 0.374392i
\(567\) 0 0
\(568\) −5.83702 + 10.1100i −0.244916 + 0.424207i
\(569\) −32.2230 −1.35086 −0.675430 0.737424i \(-0.736042\pi\)
−0.675430 + 0.737424i \(0.736042\pi\)
\(570\) 0 0
\(571\) −7.39249 −0.309366 −0.154683 0.987964i \(-0.549436\pi\)
−0.154683 + 0.987964i \(0.549436\pi\)
\(572\) −13.3213 + 23.0731i −0.556991 + 0.964737i
\(573\) 0 0
\(574\) −0.502247 0.869917i −0.0209634 0.0363096i
\(575\) 0.216041 0.374194i 0.00900952 0.0156049i
\(576\) 0 0
\(577\) 3.03682 0.126425 0.0632123 0.998000i \(-0.479865\pi\)
0.0632123 + 0.998000i \(0.479865\pi\)
\(578\) −30.5340 −1.27005
\(579\) 0 0
\(580\) 3.37205 + 5.84056i 0.140017 + 0.242516i
\(581\) −55.0410 −2.28349
\(582\) 0 0
\(583\) −11.7618 20.3720i −0.487124 0.843723i
\(584\) −8.11773 + 14.0603i −0.335914 + 0.581820i
\(585\) 0 0
\(586\) 20.9416 36.2719i 0.865089 1.49838i
\(587\) −7.96968 + 13.8039i −0.328944 + 0.569748i −0.982303 0.187301i \(-0.940026\pi\)
0.653359 + 0.757048i \(0.273359\pi\)
\(588\) 0 0
\(589\) 0.654040 + 2.50046i 0.0269492 + 0.103030i
\(590\) 6.18877 0.254788
\(591\) 0 0
\(592\) 16.3804 28.3718i 0.673232 1.16607i
\(593\) 13.2914 + 23.0213i 0.545811 + 0.945373i 0.998555 + 0.0537322i \(0.0171117\pi\)
−0.452744 + 0.891640i \(0.649555\pi\)
\(594\) 0 0
\(595\) 0.0991765 + 0.171779i 0.00406584 + 0.00704224i
\(596\) 25.4705 1.04331
\(597\) 0 0
\(598\) 1.93384 + 3.34951i 0.0790806 + 0.136972i
\(599\) 18.8742 + 32.6911i 0.771181 + 1.33572i 0.936916 + 0.349554i \(0.113667\pi\)
−0.165736 + 0.986170i \(0.553000\pi\)
\(600\) 0 0
\(601\) −16.9222 −0.690269 −0.345134 0.938553i \(-0.612167\pi\)
−0.345134 + 0.938553i \(0.612167\pi\)
\(602\) −18.4185 31.9018i −0.750682 1.30022i
\(603\) 0 0
\(604\) 9.17476 + 15.8911i 0.373316 + 0.646601i
\(605\) −3.99037 + 6.91153i −0.162232 + 0.280994i
\(606\) 0 0
\(607\) 36.3712 1.47626 0.738131 0.674658i \(-0.235709\pi\)
0.738131 + 0.674658i \(0.235709\pi\)
\(608\) 18.9545 18.7298i 0.768708 0.759593i
\(609\) 0 0
\(610\) −3.87496 + 6.71162i −0.156892 + 0.271746i
\(611\) −27.6305 + 47.8574i −1.11781 + 1.93610i
\(612\) 0 0
\(613\) −3.66105 + 6.34113i −0.147869 + 0.256116i −0.930439 0.366446i \(-0.880575\pi\)
0.782571 + 0.622561i \(0.213908\pi\)
\(614\) −7.62936 13.2144i −0.307896 0.533291i
\(615\) 0 0
\(616\) 20.6511 0.832057
\(617\) 4.91459 + 8.51233i 0.197854 + 0.342693i 0.947832 0.318769i \(-0.103269\pi\)
−0.749978 + 0.661462i \(0.769936\pi\)
\(618\) 0 0
\(619\) 8.29932 0.333578 0.166789 0.985993i \(-0.446660\pi\)
0.166789 + 0.985993i \(0.446660\pi\)
\(620\) −0.727729 −0.0292263
\(621\) 0 0
\(622\) 4.08092 7.06836i 0.163630 0.283415i
\(623\) 19.0894 + 33.0639i 0.764802 + 1.32468i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −33.8868 −1.35439
\(627\) 0 0
\(628\) −0.0980355 −0.00391204
\(629\) −0.192284 + 0.333046i −0.00766688 + 0.0132794i
\(630\) 0 0
\(631\) 21.4448 + 37.1435i 0.853705 + 1.47866i 0.877841 + 0.478952i \(0.158983\pi\)
−0.0241360 + 0.999709i \(0.507683\pi\)
\(632\) 5.05693 8.75885i 0.201154 0.348409i
\(633\) 0 0
\(634\) −34.5577 −1.37246
\(635\) 15.6963 0.622887
\(636\) 0 0
\(637\) −11.6114 20.1116i −0.460061 0.796850i
\(638\) −43.0076 −1.70269
\(639\) 0 0
\(640\) −5.13806 8.89938i −0.203100 0.351779i
\(641\) −11.2034 + 19.4048i −0.442507 + 0.766444i −0.997875 0.0651607i \(-0.979244\pi\)
0.555368 + 0.831605i \(0.312577\pi\)
\(642\) 0 0
\(643\) −2.71105 + 4.69568i −0.106914 + 0.185180i −0.914518 0.404544i \(-0.867430\pi\)
0.807605 + 0.589724i \(0.200763\pi\)
\(644\) −0.905427 + 1.56824i −0.0356788 + 0.0617975i
\(645\) 0 0
\(646\) −0.323544 + 0.319708i −0.0127297 + 0.0125787i
\(647\) −25.1940 −0.990477 −0.495238 0.868757i \(-0.664919\pi\)
−0.495238 + 0.868757i \(0.664919\pi\)
\(648\) 0 0
\(649\) −7.50430 + 12.9978i −0.294570 + 0.510210i
\(650\) −4.47564 7.75203i −0.175549 0.304060i
\(651\) 0 0
\(652\) −11.3431 19.6469i −0.444231 0.769431i
\(653\) −8.11903 −0.317722 −0.158861 0.987301i \(-0.550782\pi\)
−0.158861 + 0.987301i \(0.550782\pi\)
\(654\) 0 0
\(655\) 5.86776 + 10.1633i 0.229272 + 0.397112i
\(656\) −0.405129 0.701703i −0.0158176 0.0273969i
\(657\) 0 0
\(658\) −68.0357 −2.65231
\(659\) −6.73290 11.6617i −0.262277 0.454277i 0.704570 0.709635i \(-0.251140\pi\)
−0.966847 + 0.255358i \(0.917807\pi\)
\(660\) 0 0
\(661\) −4.51947 7.82796i −0.175787 0.304472i 0.764646 0.644450i \(-0.222914\pi\)
−0.940433 + 0.339978i \(0.889580\pi\)
\(662\) −8.52701 + 14.7692i −0.331412 + 0.574022i
\(663\) 0 0
\(664\) −22.3743 −0.868289
\(665\) −14.3543 3.93811i −0.556634 0.152713i
\(666\) 0 0
\(667\) −1.18715 + 2.05620i −0.0459665 + 0.0796163i
\(668\) −11.4653 + 19.8585i −0.443606 + 0.768348i
\(669\) 0 0
\(670\) 6.09394 10.5550i 0.235429 0.407776i
\(671\) −9.39729 16.2766i −0.362779 0.628351i
\(672\) 0 0
\(673\) 13.6988 0.528048 0.264024 0.964516i \(-0.414950\pi\)
0.264024 + 0.964516i \(0.414950\pi\)
\(674\) −21.3517 36.9823i −0.822438 1.42450i
\(675\) 0 0
\(676\) 14.5157 0.558298
\(677\) 11.6030 0.445941 0.222970 0.974825i \(-0.428425\pi\)
0.222970 + 0.974825i \(0.428425\pi\)
\(678\) 0 0
\(679\) 15.2762 26.4591i 0.586246 1.01541i
\(680\) 0.0403154 + 0.0698283i 0.00154602 + 0.00267779i
\(681\) 0 0
\(682\) 2.32039 4.01904i 0.0888524 0.153897i
\(683\) 25.5290 0.976840 0.488420 0.872609i \(-0.337574\pi\)
0.488420 + 0.872609i \(0.337574\pi\)
\(684\) 0 0
\(685\) −10.2572 −0.391908
\(686\) −7.17528 + 12.4279i −0.273953 + 0.474501i
\(687\) 0 0
\(688\) −14.8570 25.7330i −0.566416 0.981062i
\(689\) −13.4518 + 23.2993i −0.512474 + 0.887631i
\(690\) 0 0
\(691\) −46.1415 −1.75530 −0.877652 0.479298i \(-0.840891\pi\)
−0.877652 + 0.479298i \(0.840891\pi\)
\(692\) 10.5515 0.401106
\(693\) 0 0
\(694\) 25.1631 + 43.5838i 0.955178 + 1.65442i
\(695\) 21.8088 0.827255
\(696\) 0 0
\(697\) 0.00475566 + 0.00823705i 0.000180134 + 0.000312000i
\(698\) −0.00862000 + 0.0149303i −0.000326272 + 0.000565119i
\(699\) 0 0
\(700\) 2.09550 3.62951i 0.0792024 0.137183i
\(701\) 0.219837 0.380768i 0.00830312 0.0143814i −0.861844 0.507173i \(-0.830690\pi\)
0.870147 + 0.492792i \(0.164024\pi\)
\(702\) 0 0
\(703\) −7.30277 27.9192i −0.275429 1.05299i
\(704\) −4.73024 −0.178277
\(705\) 0 0
\(706\) 5.46650 9.46826i 0.205735 0.356343i
\(707\) −3.73997 6.47782i −0.140656 0.243624i
\(708\) 0 0
\(709\) 19.4677 + 33.7191i 0.731125 + 1.26635i 0.956403 + 0.292051i \(0.0943377\pi\)
−0.225278 + 0.974295i \(0.572329\pi\)
\(710\) −15.1084 −0.567007
\(711\) 0 0
\(712\) 7.75988 + 13.4405i 0.290814 + 0.503704i
\(713\) −0.128100 0.221876i −0.00479739 0.00830932i
\(714\) 0 0
\(715\) 21.7081 0.811835
\(716\) −3.78373 6.55361i −0.141404 0.244920i
\(717\) 0 0
\(718\) −16.0073 27.7255i −0.597388 1.03471i
\(719\) −11.5179 + 19.9496i −0.429546 + 0.743995i −0.996833 0.0795252i \(-0.974660\pi\)
0.567287 + 0.823520i \(0.307993\pi\)
\(720\) 0 0
\(721\) −35.8219 −1.33408
\(722\) 0.407100 34.1305i 0.0151507 1.27021i
\(723\) 0 0
\(724\) −12.3092 + 21.3202i −0.457469 + 0.792360i
\(725\) 2.74750 4.75882i 0.102040 0.176738i
\(726\) 0 0
\(727\) 22.2700 38.5727i 0.825948 1.43058i −0.0752445 0.997165i \(-0.523974\pi\)
0.901193 0.433419i \(-0.142693\pi\)
\(728\) −11.8092 20.4542i −0.437678 0.758081i
\(729\) 0 0
\(730\) −21.0117 −0.777677
\(731\) 0.174401 + 0.302071i 0.00645044 + 0.0111725i
\(732\) 0 0
\(733\) 34.2392 1.26465 0.632326 0.774702i \(-0.282100\pi\)
0.632326 + 0.774702i \(0.282100\pi\)
\(734\) −8.80612 −0.325040
\(735\) 0 0
\(736\) −1.32072 + 2.28756i −0.0486826 + 0.0843207i
\(737\) 14.7786 + 25.5974i 0.544378 + 0.942891i
\(738\) 0 0
\(739\) 2.42166 4.19444i 0.0890823 0.154295i −0.818041 0.575160i \(-0.804940\pi\)
0.907123 + 0.420865i \(0.138273\pi\)
\(740\) 8.12555 0.298701
\(741\) 0 0
\(742\) −33.1230 −1.21598
\(743\) 6.53384 11.3169i 0.239703 0.415178i −0.720926 0.693012i \(-0.756283\pi\)
0.960629 + 0.277834i \(0.0896165\pi\)
\(744\) 0 0
\(745\) −10.3765 17.9727i −0.380167 0.658468i
\(746\) 11.6766 20.2245i 0.427512 0.740473i
\(747\) 0 0
\(748\) 0.310591 0.0113563
\(749\) 46.7519 1.70828
\(750\) 0 0
\(751\) −4.24060 7.34493i −0.154742 0.268020i 0.778223 0.627988i \(-0.216121\pi\)
−0.932965 + 0.359967i \(0.882788\pi\)
\(752\) −54.8798 −2.00126
\(753\) 0 0
\(754\) 24.5937 + 42.5975i 0.895648 + 1.55131i
\(755\) 7.47548 12.9479i 0.272061 0.471223i
\(756\) 0 0
\(757\) 17.6798 30.6223i 0.642583 1.11299i −0.342271 0.939601i \(-0.611196\pi\)
0.984854 0.173386i \(-0.0554707\pi\)
\(758\) −15.0286 + 26.0303i −0.545864 + 0.945464i
\(759\) 0 0
\(760\) −5.83502 1.60085i −0.211659 0.0580688i
\(761\) −19.8496 −0.719547 −0.359773 0.933040i \(-0.617146\pi\)
−0.359773 + 0.933040i \(0.617146\pi\)
\(762\) 0 0
\(763\) −24.1657 + 41.8562i −0.874856 + 1.51529i
\(764\) 10.4752 + 18.1435i 0.378978 + 0.656409i
\(765\) 0 0
\(766\) −26.8503 46.5061i −0.970141 1.68033i
\(767\) 17.1652 0.619798
\(768\) 0 0
\(769\) −2.82265 4.88897i −0.101787 0.176301i 0.810634 0.585553i \(-0.199123\pi\)
−0.912421 + 0.409253i \(0.865789\pi\)
\(770\) 13.3632 + 23.1457i 0.481575 + 0.834113i
\(771\) 0 0
\(772\) 8.92444 0.321198
\(773\) 24.6102 + 42.6260i 0.885166 + 1.53315i 0.845523 + 0.533938i \(0.179289\pi\)
0.0396424 + 0.999214i \(0.487378\pi\)
\(774\) 0 0
\(775\) 0.296472 + 0.513505i 0.0106496 + 0.0184456i
\(776\) 6.20979 10.7557i 0.222918 0.386106i
\(777\) 0 0
\(778\) 57.0088 2.04387
\(779\) −0.688308 0.188838i −0.0246612 0.00676583i
\(780\) 0 0
\(781\) 18.3199 31.7310i 0.655539 1.13543i
\(782\) 0.0225441 0.0390475i 0.000806175 0.00139634i
\(783\) 0